2. Description Of Prior Art
Presently all relatively efficient axial fluid flow devices in general use are based on the conventional propeller. All such devices function by accelerating or decelerating fluid mass using blades mounted upon an axis and subsequently rotated. Due to the differences in rotational velocity of blade elements at the differing radial locations of such a blade, various locations therefore encounter flow from various directions.
As is evident in FIG. 1 of prior art, these blades need therefore to be continuously twisted as well as variously shaped along their length in order to compensate for these differences in velocity and resultant vector 10 of the oncoming flow.
The top illustration of FIG. 2 demonstrates that since the resulting fluid force on the blade at a given location is approximately perpendicular to the direction of incoming flow, this twisting results in physical forces whose directions vary in their usefulness in providing the intended axial change of momentum of this fluid.
As shown in the middle of FIG. 3, since in addition to orientation, the force on any blade section varies as the square of the local velocity as well, most purely axial thrust of fluid in the swept disc occurs in a relatively small annulus close to the blade tips 12 where fluid dynamics recognizes unavoidable flows that result in loss of thrust and formation of tip vortices 14 that due to their high transverse velocities, continuously dissipate kinetic energy and physically drag along vortex structures.
As shown in the lower illustration of FIG. 2, since drag due to—and induced by—lift in any tipped foil results in an increase of fluid acceleration—called induced downwash 15—inboard of the tip to offset the pressure lost to vortex formation at the tip, the disadvantageous helix angles 16 of FIG. 3 on the left of the inboard portion of the propeller disc spills significant energy by twisting the slipstream 18 out of desired axial alignment resulting in root vortex losses. This loss is much beyond that of the drag caused by purely frictional entrainment of rotation.
As seen in FIG. 13a, another consequence of the described tip vortex low-pressure wake structures that develop after passage of the foil is the lateral divergence of flow potential between the upper and lower trailing edge, causing flows to deviate toward the lines of very low equipotential pressure of the developing tip vortex behind the tail. As particles leave the tail, this divergent potential causes the upper and lower particles to approach and embrace in a suddenly tightening radius of curvature by way of the conservation of angular momentum. This results in powerfully rotating vortices of path-transverse vector forming the so-called vortex sheet of discontinuity, which attaches itself to the trailing edge via these filaments' commensurately powerful suction cups, dragging some of these structures—and their fluid mass entrainments—along for the ride.
In the case of the conventional wind turbine, the highly loaded annulus 12 of FIG. 3 additionally imposes the characteristic uneven retardation on the flow streamlines on the right of FIG. 3, causing significant swirl and a thick sheet of discontinuity resulting in the well-documented spillage of over half the theoretically available linear kinetic energy.
These vortex flows 14 additionally also have the disadvantage of causing very high tip region spanwise flows and actual reversals of flow as shown on top of FIG. 9 with resulting boundary layer turbulence, loss of lift and low pressures that additionally occasion different design constraints in different applications:
Ship's propellers—high tip velocities causing cavitation in the tip area engendering destructive interblade harmonics, vibration, resonance and blade erosion, appendage and hull resonance
Airplane propeller—the propeller is primarily speed limited by the severe drag rise of the transonic boundary layer separation shock wave induced by the tip flows exceeding the speed of sound at even moderate subsonic velocities and occasioning noise and buffetHelicopter blade—even though the helicopter disc is not purely an axial flow device it nevertheless encounters similar constraints: vortex noise, blade slap due to vortex buffeting and harmonic and resonant oscillations due to rapidly changing differential pressures across the disc due to uneven pressure distribution.Additional important factors that state added sources of loss of efficiency that affect the conventional propeller are:The inescapable fact that due to said blade dynamics, the slipstream contracts significantly before and after it laves the theoretical disc of actuation—the Froude Disc of Momentum Theory 19—of the middle of FIG. 2 that represents the plane of rotating blades 20. This is seen as a significant inflow at the propeller tip 22, and locally out of alignment with intended axial acceleration. This has the effect of diminishing the size of the effective actuator disc and so decrements the mass that it can accelerate relative to its theoretical value.
Also, since the propeller works by generating differential pressures across this disc area, a sharply contracting slipstream implies lower pressure differentials 24 across the disc than an actuator disc that had means to benefit from or ameliorate such contraction.
Since—according to Propeller Momentum Theory—efficiency is developed, and measured by the momentum change involving the highest possible fluid mass involving the smallest possible velocity change 26, this unopposed contraction—or its expansion in the case of the turbine—, must also be considered a source of inefficiency through the resulting decremented mass flow rate in the conventional propeller.
An important structural limitation that results from this blade fluid dynamic that detracts from efficiency is the fact that structurally, a thin, twisted rotating bar of relatively flexible material somewhat akin to a single prong long tuning fork—of low natural frequency—, has low resistance to Coriolis forces, disc loading asymmetry, torsional, resonant and harmonic oscillation and so needs a massive and fluid-dynamically inefficient blade root.
An additional fact is that the requirement of adequate starting performance combined with good cruise performance occasions cruise speed efficiency compromises caused by the propellers stated severe design constraints.
In spite of their shortcomings, propellers enjoy the considerable advantage of a precise and repeatable method of design that has allowed a long history of incremental improvement and increasingly high precision of manufacture, in an engineering discipline where minute variations of shape have surprisingly large effects on performance. This method of design represents a continual refinement of theories that have been in existence for most of a century.
One of these theories in wide use—the Blade Element Theory—analyzes velocity vectors and viscosity coefficients of individual blade sections at successive blade radii and computes the entire propellers parameters by summing the individual parameters of these elements.
Instead of using the plane aligned with vectors of predominant flow, such methods model actual blade flows by computed changes of momentum along theoretical tangents to helices inscribed on surfaces of revolution generated by blade element motion as reference datum.
Although no rigorous analysis of actual three-dimensional vortex formation is made, a well documented database of empirical values for secondary flows provide the correctional factors that enable today's high correlation of theoretical and experimental values.
Importantly, these theories work with assumptive linear and statistical parameters of free stream velocity without a time-based rate of change reference frame.
These methods assess theoretical conditions of statistical, time invariant steady-state lift on rigid foils that move along helices in Euclidean space as shown in FIG. 4a. 
As consequence of this, the vector and time coefficients of the Impulse—Momentum Equations of Motion—, which the equation of Blade Element of Lift does not formally treat, except for an invariant velocity of inflow—introduce highly skewed inflows in the case of rotation.
As is depicted in the lower illustration of FIG. 2, bound vortex upwash is a function of time. Its prerequisite—the acceleration of fluid mass ahead of its path by the strong attractive force of its low-pressure isobars of potential is normal to lines of equipotential pressure as shown in lower left of FIG. 3. Because this force is a vector, rotation, which can only affect regions of fluid mass over a diffusing sector, involving the rate-of-change tangent-sector of the swept angle of tangential motion, this helical path must itself also be considered a source of propeller inefficiency. According to Newton's second law, a given change in momentum due to any given force-vector is a function of the relative duration of this force. The described sector of diffusion attending rotation must therefore have weak axial stream-tube-relative influence, compared to the steady duration of linear axial-plane motion.
A propeller blade section low-pressure force field of curved path of the lower left of FIG. 3 has not had time to accelerate the actually encountered incoming fluid particles as it diffuses the influence of its low pressure isobars to particles along the diffusion-arc of the changing vector-tangent of its curved path, to particles outside its path, particles that it will not actually encounter. Rotational devices that don't compensate for this curved path must therefore experience a deficit of inflow velocity and weak upwash as shown in FIG. 4a and therefore must be assumed not to benefit from the early phases of the upwash/downwash cycle of what is, in effect, a special wave system called the bound vortex. Such devices accordingly must operate in their own downwash, behind the wave crest.
To crudely illustrate schematically these implications' bearing on the relative efficiency of helical versus linear motion on the basis of glide angle, sailplanes with their slender wings having a nearly horizontal glide angle, even the Space Shuttle with its delta planform and high tip losses at 19 degrees glide angle is more efficient than the streamlined helicopter with a steeper autorotation descent angle using foils that are even more slender than those of sailplanes.
To sum the described deficiencies of rotation itself, partly owing to the continuing inscrutability of the phenomenon of turbulence, and partly due to the millennial legacy of rotation itself, is the practice of this art presently not well integrated with the more evolved time-domain practices in related fields that successfully apply the laws of physics of waves and oscillating systems. As a consequence, the just described inefficiency of helical motion artifacts and tipped-blade vortex that limit economic cost-benefit has been generally considered unamenable.
Due to sum of these well-documented disadvantages attending rotation, there have been many attempts to introduce devices to the marketplace that deal with one or more individual symptoms of the described problem syndrome. Among these are strategies to eliminate tip losses through blades forming centrifugal catenary half-loops, or to simply convert rotary motion to linear motion through rotor blades in the shape of segments of spirals, using the property of the boundary layer that can obscure the resulting ‘virtual’ motion's different flow directions via the many thin lubricating layers sliding over each other. This would be analogous to a rotating spiral worm gear that can transmit linear motion to its conjugate rack, as shown in FIG 8e. Others have attempted to prevent spanwise flows through chordwise corrugations parallel to flow in an attempt to prevent the lateral divergence pre-conditions of vortex development.
The subject of this document incorporates similar strategic synergies among others using tools provided by several modern time-domain disciplines. In addition it employs direct means to amend the phenomenon of the highly pulsating and directionally disordered reaction mass of the wake that all of these devices are subject to, and that according to the equations of motion, must be considered a measure of lost linear momentum,
To explain these strategies and their indispensability to these proposed devices, I now provide a brief overview.
Time-invariant methods of analysis are particularly ill adapted to analyze forces resulting from unusual—namely linear wave propagation—anguillar propulsive mechanisms, particularly those of nature. Here all such mechanisms involve time-domain oscillations and flexing of propulsive elements undergoing variable rates of change. Such rates of change become evident when sectioned by reference planes aligned with their primary axis of motion, and normal to their transverse undulations as shown in FIG. 4b. This motion can be analyzed by comparing the time-regressed body outlines to time-samples of body-relative isocline acceleration and traveling inclined plane maxima as shown in FIG. 4c. Such motion promises high efficiencies, as carangiform swimmers have been clocked at velocities that theory predicts to be unattainable for them.
For lack of comprehensive tools, however, previous attempts to introduce mechanical analogs of such promisingly efficient motions of nature as propulsive devices to the marketplace have suffered from inadequate precision of analysis, thus predictable manufacture, and have—so far—have been commercial failures.
As a three-dimensional secondary flow with its many degrees of freedom is at present treated as heterogeneous turbulence by accepted practice, translation, sliding, flexing and undulation are also not rigorously modeled to acceptable standards of engineering practice. The economic investment necessary to generate such theoretical models of nature has not yet been generally made available.
Thus, any motion that results in undulation as generated by rotation must involve highly complex compound artifacts involving changing reference frames and boundary layer interactions that pose severe analytic difficulties using state of the art design tools.
Historically, there have been some attempts to introduce devices based on the animal model of locomotion to accelerate or decelerate fluid in the hope to improve upon the propeller. In particular, many of these have attempted to generate relative motions along various versions of the spiral of changing radius. The patents of Haussmann—1895—and Sugden—1970—in particular showed the structural advantages of spiral foil segments joined at their tips.
Such devices, especially the Sugden device promoting ‘undulating flow’, claimed to demonstrate improved efficiencies in comparison to the propeller.
Such devices in rotation, however, use:
Constantly changing foil profile elements
Constantly changing foil geometry like camber, length, thickness,
Continuously varying rate of change of lift coefficient, (angle of attack)
Continuously shed vortices attendant to such change in angle of attack
Constantly changing compound sweep, and high spanwise flow
Constantly changing flow directions not aligned with a surface of revolution—the
theoretical plane of analyses—
Constantly changing boundary layer differential shear with vectors not aligned
with the primary dynamic flow field,
Constantly varying viscosity coefficients,
Rapid reversal of motion,
Rapid reversal of wake vortex spin direction (Karman Vortex Street)
Rapid alternation of lifting surface orientation to the flow field,
Rapid reversal of flow direction
Rapid reversal of bound vortex spin direction
Rapid reversal of lift circulation co-efficient
As this latter parameter is the very basis of the classical theory of lift, any design that cannot—due to these imponderabilities—predict inflow vector, cannot determine this circulation or the force of lift, or drag.
Flow is by its very nature evasive and turbulence cascades down to infinitesimal time scales. The possible interactions with it—and possible unintended consequences thereof—are infinite. Therefore this massive analytical overload must be simplified by designing a process that is understandable to the existing tools of analysis. The main tool, Blade Element Theory, must be given reliable inflow, viscosity and blade profiles of known parameters. If lift cannot be determined, foil orientation is not precisely possible. Without formulated precision of causal relationships, repeatable effects became difficult to achieve.
Since some of such devices proposed to benefit from undulations of reaction masses however, they must be presumed to experience undulations of time-domain inflow vectors that demonstrate continuous rates of change of kinetic and potential energy. Without a fully rigorous fluid dynamic modeling of such flows—still out of reach—, relative motion could not be determined. Such devices' orientation to flow and thus pressure gradients could not be ascertained to satisfy the Blade Element Theory requirements as well as standards of manufacturing repeatability.
Without time-domain inflow parameters, such attempts were limited to intuitive experimentation on the basis of trial-and-error and as commercial devices could not hope to compete with the considerable empirical theoretical database of a highly refined engineering practice benefiting from many decades of incremental data refinement.
And yet, accurate velocimetry analysis as to the effect of time-domain and boundary layer phenomena have been available in the field of Biofluiddynamics and certainly do now exist. Recent government sponsored university research advances in the field of mathematical biofluiddynamics using high-speed video image Digital Particle Laser Doppler velocimetry provide a relatively accurate model of the boundary layer, mechanics and vector fields of time-evolving vortex dispositions of animal undulatory expanding wave locomotion. To make a computational model of such motion, all that is additionally needed once viscosity and thus shear-drag is determined, is wave mechanics itself to relate energy content and orbital inflow.
Thus experimental computational three-dimensional vector-field animations of fish propulsion have been, and are now widely available.
If such insights into the vector field dispositions and boundary layer ejection mechanisms enabling aquatic creatures their extraordinary reductions of form drag and paradoxical speed/power relationships could somehow be practically applied to the rotational mode of operation, then my primary avocation, namely that of creating efficient wind power devices, might benefit from the prospect of recapturing some of that half-portion of linear momentum that is presently made unavailable using conventional means.
With this prime aim in mind, I determined to examine the axial shear-plane-relative motion of rotors made of wave-cycle profile sequences arrayed around 3D spiral segments, remapped to truncated cones, that act the part of time-domain cams. This is illustrated on the right of FIG. 5c. FIG. 5b shows the enabling lubricity mechanism conferred by the boundary layer that allows axially aligned stream tubes to be relatively unaffected by tangential ‘vector shear’.
These path-oriented profile sequences would sequentially progress along a constant angle to this path at constant velocity along both dimensions of the axial shear plane by shearing through all encountered axial planes—and thus any datum reference plane—moving tangential to that plane. They would additionally eject boundary layer accumulations by creating high-rate expanding-wave anguillar propulsion through the effect of the rate-of-change Inclined-Ramp contour variations that the smoothed after-body profile sequences transmitted, as they transited the shear plane. By varying the spiraling rotor ‘blade’ as a whole by such parameters as profile length, radius, angular velocity and axial and radial advance, it would be possible to achieve structural load paths embedded within this rotor ‘blade’ that came close to the structurally advantageous centrifugal catenary curve. Thus, the analytical imponderables of undulation of inflow and reaction mass, as well as the time-domain effect of unknown profile-section change sequences of unknown parameter would simply be bypassed, allowing a systematic periodic function based progressive remapping of a single published profile, which can, over a single wave cycle, be deemed regressed—and thus in its effect equal to—to its published coordinates and thus performance curves.
Because this concept seemed also to contain disquietingly paradoxical, and even mutually exclusive operating modes, namely that a rotating device, while imparting angular momentum, should at the same time be one that guides and benefits from a bound vortex wave system moving along straight lines, I proceeded to the create the bridging concepts, computer models and finally actual devices to convince myself that rotation can indeed, produce linear bound vortex pressure wave motion substantially parallel to the axial shear plane, as long as the velocity vectors along this plane are greater than that of the engendering local tangential velocity of rotation.
I also established to my satisfaction that—in the case of such motion and adequately high Reynolds number—simplifying the tangential shear effect of the multiplicity of incoming axial stream tubes to a single schematic axial shear plane provides the bridging concept enabling a good predictive Blade Element-Theory based correlation with the measured flow of actual devices.
Accordingly, I will now outline the advantage of these bridging concepts.
The Proposed Invention as an Advance in the State of the Art
These devices propose to advance the art of extracting momentum from—or imparting momentum to—axial flow, by ordering the directionally chaotic and pulsatile reaction mass of the wake of current rotational and spiral-based devices using several synergistic strategies, each of which are of advantage in analysis of spiral-based devices operating in the time domain. They depend on the two main enabling phenomena. The first is the lubricity of the many layers of fluid that cling to any dynamic shape called boundary layer.
As is shown in FIG. 5b, any embodied fluid dynamic shape—here a spinning saucer shaped toy disc that provides lift is accompanied by a field of flow streamlines, that delineate local fluid motion. The main features of this vector field are:    1. The dynamic flow providing the pressure differentials that generate useful forces    2. The frictional adhesions including standing vortices 30 entrained by this body    3. The roiling vortex wake representing the lost frictional energies that represent the cost of sustaining such motion.
Surrounding this body is an exceedingly thin membrane 31—the boundary layer—. This layer enables a kinetically economical passage for that vast majority of much faster particles of high kinetic energy making up the ‘dynamic flow’ that is the actual generator of the pressure differentials that create useful forces.
This phenomenon is illustrated by the flight of the tossed and rotating disc whose dynamic flow field is here illustrated. Even though most of its surface is moving in directions at variance with the path of its flight, the phenomenon of lubricity-masked directional boundary layer ‘vector-shear’ nevertheless enables the characteristic dynamic flow field that enables all linear dynamic flight, that results in its amazing feats of stability and length of flight.
The second phenomena that enables this phenomenon for this toy disc—or any-devices that rotate in order to impart or extract momentum, is the overwhelming collective enmeshed inertia of the continuum of axially aligned mass flow that shows quantifiable resistance to being tangentially twisted as a result of the rotation. This resistance itself enables analysis along reliable helices of relative motion of FIG. 4a in conventional devices. This fact allows the collective multiplicity of coaxial planes of motion to be reduced to a single theoretical Plane-of-Shear through which all these devices—whether conventional or not—must, by definition, ‘shear through’. Therefore:                1. In order to function as an improvement over propeller-based devices, any spiraling or catenary-loop shear device must first be able to specify the amount of shear plane twist the device is expected to generate, lest inflow vector becomes indeterminate. For this, conventional Reynolds number-based practice, using the three-dimensional Galilean form of the Navier-Stokes equations serves to estimate total shear stress influence on this plane, its cost in turning moment work and resulting tangential motion of the reaction mass. This form of the equation offers implicit compensation for differences in boundary layer vector that translate these to a helically oriented velocity gradient resulting in a ‘stress’ coefficient within the boundary layer itself. This is illustrated by the left sequence of FIG. 4d. As the Navier Stokes equations confine themselves to measure velocity-gradient-based momentum transfer from layer to layer of this thin lubricating envelope, and the final outermost layer must therefore be presumed aligned to the dynamic flow, the cross-section of the illustrated annular wing with its dynamic flow streamlines would show no difference between static and rotating states—by hypothetical frictionless means—except for the shedding intensity of the trailing vortex system, as intra-boundary layer particles experience a greater path length, mixing length and momentum loss. This lost kinetic energy must be borrowed from mass-momentum of the energetic outer layers. This borrowed extra mass accumulates, now having lost momentum, and is episodically ejected at the tail into time-topology vortex structures that reflects this longer path length coefficient. The work of turning has thus been transferred to the boundary layer in the form of minute polarized angular momentum, which is ‘spooled’ in a topological sense into asymmetric counter-rotations of a Karman Vortex Street with slowed central flow. Thus, according to classical theory itself, dynamic flow streamlines lack a direct mechanism to make them stray out of alignment with the axial plane before the trailing edge. As experience with this configuration shows, however, that the wake does in fact twist in the direction of rotation, this entrained, now co-rotating vortex sheet must be implicated in this twist, namely by the secondary momentum transfer of the velocity-gradient-based mechanism of this same theory. The vortex sheet is deemed ‘attached’ to the trailing edge and rotated along, importing momentum from the energetic interface and pulling and twisting this flow—and thus the shear plane itself—through the same momentum transfer. Thus, for any shear-plane-active spiral devices to offer any advantage at all, they must first address shear-plane-distortion by detaching this vortex sheet. This is the central strategy of the proposed class of devices. Thus the prime enabling mechanism of the device is the detachment of this ‘drag’ entrainment through shape sequence anguillar propulsion.        2. Compound and variable planform sweep of the rotor ‘blade’—as imposed by the embedded 3D spiral ‘time-cam’—imposes well-documented disadvantageous spanwise flows and high form drag at economically useful lift coefficients that would negate much of the theoretical advantage of the proposed devices, impose high rate-of-change variations in circulation and lift and thus create unacceptable boundary layer turbulence drag as well as a low lift curve slope. As these phenomena are mainly due to adverse tail section pressure gradients, I determined to enlist the mechanism of anguillar propulsion to enforce tail region small-wave chordwise near-wake and boundary layer acceleration and expulsion in order to reduce pressure gradients and enforce axial plane flow alignment. This required time-domain analysis of animal modes of locomotion that involve oscillation using analysis of isocline travel of body wave and surface inclination. This is performed using a datum plane containing the primary axis of locomotion and transverse flexing vectors.        3. This schematic additionally uses energy-content wave equation analysis, the phase plane analysis of oscillations for dissipation and resistance to flow-rate-of-change, or ‘hysteresis’, and Strouhal number to determine phase, frequency, amplitude and isocline rate-of-change of body sections engaged in wave-like transformations.        
In these methods, flexing propulsive bodies including fins and wings are frequency-sampled for rate-of-change differential motion normal to and along their axis of symmetry.
It is the synergy of these time-domain strategies that result in final device shapes specified by time-domain mathematics. These demonstrate a considerable theoretical advance in efficiency.
To specify this advantage I will now compare theoretical considerations of state-of-the-art and the proposed devices' functional basis using schematic and graphical metaphor to illustrate the classical-parameter-relative implications derived from Blade Element and Momentum Theory.
Theory of Operation
Although the fluid dynamic lift equation itself contains no time coefficients—except for inflow velocity—, it nevereless is historically derived from Newton's time-domain equations of motion. This fact has important bearing on the implications resulting from the rotation of lift-producing blade elements.
Accordingly, the proposed devices' design methods re-import time-domain impulse-momentum considerations from these original equations, as the after-body of conventional profiles is presently design-constrained by the need to limit adverse pressure gradients in order to regain free stream velocity and so prevent the spanwise detachment of flow.
In principle, impulse-momentum-based interventions using path-transverse Inclined-Plane-based, body-relative traveling waves—as documented to be highly effective in reducing such adverse pressure gradients in the motions of aquatic creatures—are readily available to re-import energy to this tail region using Inclined Plane space quadrature vector-coupling. These are mechanisms that have analogs in the motion of worm/linear rack conjugate enmeshment that translates rotary to linear motion, where the ‘sliding’ component of motion is largely eliminated by a suitable lubricating agent.
These devices thus benefit from mechanisms implicit in the Equations of Motion's impulse generating rate-of-change-inclination of surfaces the tangential motion component of which is masked by the path-compensating lubrication-conferring mechanisms of the boundary layer, when computed relative to the axial shear plane.
These mechanisms thus, in effect, duplicate the serial metamorphosis of traveling wave anguillar phased shape change resulting in its well-researched phase-related traveling pressure wave propulsion.
Such serial transformations of a body classifies any such time-regressed section of this body as a “Soliton Meta-Element”, a term of convenience that derives from the notion that a physical form engaged in a rate-of-change wave-like metamorphosis has an effect beyond its moment-to-moment aspect of physical undulation but is part of a fluid-wide continuum of self-stabilizing processes, a single wave meta-phenomenon encompassing a fluid-wide system of angular momentum orbital flows.
It can be therefore treated as part of a single dissipative oscillating system, slowly decaying on the time axis behind its origin-of-resonance. Accordingly, rough estimates as to speed, dissipation and energy budget can be deduced from the observed, or desired, coefficients of the wave equation.
Much is not explained by such a view, but being a concept of convenience gives it the considerable advantage of being able to ignore the many factors of mitigation and nuance that have—according to this view—considerably less immediate bearing.
It merely observes the fact that the eel, for example, is seen to proceed at a speed through the water that is related to the frequency and amplitude terms of a periodic function, as well as the expanding amplitude and expanding distances between the body-relative traveling curvature-isoclines of its body coils.
This concept thus provides a crude scheme not only for the analysis of fish and bird propulsion, but any other fluid induced oscillation, including such widely divergent phenomena such as flutter, vortex induced resonance, or any other oscillation of natural flows and their effect on physical surfaces. As shown in FIG. 4c, all such motion is characterized by the rhythmic undulations of form-conferring envelopes and their wake vector fields moving in time with the undulating envelope shapes that give rise to them. All display the characteristic progressive phases of a periodic waveform.
As is well documented by velocimetry analysis, this waveform extends well behind the undulating body itself into the characteristic regions of undulating accelerated—or decelerated—central flows bounded by standing vortices of alternating polar rotations called Karman Vortex Street.
As is shown in FIG. 4d, any fluid dynamic object, whether rigid or flexible, however physically shaped, is deemed enveloped by this time-based periodic fluctuation of dynamic flow. Here the flow has equipped a flagpole with closely adhering standing vortices 27, allowing fast-moving air particles outside this envelope a kinetically economical passage by conserving their momentum through pressure recovery, This results in the characteristic teardrop shape statistical envelope contours of the time-regressed dynamic flow continuum, containing within its borders these lubricity—and shape-conferring secondary flows.
The frequency of flexion of the “tail” of this flow field relates to the resonant frequency and diameter of the flow field (Strouhal number) and fluid system hysteresis, which acts as a kind of ‘streamline-inertia’, or ‘flow pattern memory’ of the oscillating system. These interrelationships, along with other factors such as viscosity, govern the observed vortex shedding frequency.
In view of these observations, and without claim of scientific rigor or even denial of the fact that propulsive foils or fins—especially for carangiform propulsion—may well be more significant for thrust as this body wave in linear propulsion, the Meta-Element concept is based on the following admittedly arbitrary working hypothesis:                1. The Meta-Element is defined as the time-average statistical contour of demarcation of the dynamic flow field 27 of FIG. 4d. All frictional secondary flows such as boundary layers—whether turbulent or laminar—or separation bubbles, or envelope shaping standing vortices, are deemed included during a full cycle of major Strouhal-Karman vortex period flexion. It retains data on the Fourier expansion of the periodic waveform for the major cycle. It abstracts energy dissipation—or import—values from the shape of the curve of envelope maxima 28 of amplitude and wavelength expansion terms.        2. It makes an assumption that if the mean chord of such Meta-Element fluid dynamic body envelopes undergo path-transverse flexions of given frequency and wavelength expansion parameters that allows such bodies locomotion—or retromotion—relative to wake vector field dispositions of FIG. 4b of similar contours but different wavelength, then it will be the Phase-Plane-Spiral logarithmic increment—or decrement—parameters of the path wave compared to the body wave that give information on the velocity as well as energy expenditure of this relative body motion. This is a concept analogous to ‘propeller slip’ and is also shown on the lower left of FIG. 7d.         3. As is well documented in above-mentioned scientific references, these parameters include, but are not limited to, wavelength, frequency, and amplitude of flexion. Since the fluid medium provides viscous damping, the phase-plane orbit of generation of nature is generally shown—but not limited—to be of a family of logarithmic spirals of FIG. 4c for the inertia-bound flexions of nature.        4. Information about body-relative dispositions of viscous drag is also inferred from the parameters of the Phase-Plane-Spiral of wave form generation, which are abstracted from the—usually—parabolic envelope of maxima of this expanding wave 28, as shown in FIG. 4c.         
In this way does wave form analysis, and the physics of oscillating systems result in a drag component for the body, or body element. From this, and the other known parameters of viscosity—Reynolds number—, a coefficient of drag is estimated.
Next, a time averaged full wave cycle regression of the fluctuating contours of this dynamic flow field envelope is derived from sampling intervals.
These provides the envelope and mean chord co-ordinates of a theoretical rigid foil element with parameters of drag—or thrust—that can be readily inferred and then be used to calculate the velocity and pressure gradients prerequisite to the calculation of viscous and dynamic forces.
In the case of the desired profile sequence of the proposed spiraling rotor, this hysteresis-based regression concept allows the use of conventional profiles in the public domain, treating the full cycle of transitory phase transformations as a single statistical profile of fully regressed original coordinates, allowing the use of published performance curves. A full periodic function cycle phase sequence is accordingly treated as a single ‘virtual foil’ element, —a Meta-Element—, of linear velocity and minute thrust, —as opposed to drag—. This is deemed a flexible physical membrane, aligned with axial flow, and gliding along its spiral foil-shaped timing-am and resonator phase sequence, a concept that is shown in FIG. 5c. 
I will now describe this method of generating the requisite shape change using the example of a wind turbine rotor ‘blade’ element.
The coordinates of the physical shape of a full rotor ‘blade’ are progressively developed by a periodic function-algorithm method that can be illustrated using a graphic analog of this transformation process and shown overemphasized for visual clarity on the left of FIG. 5d. Here a conventional public-domain profile is split into a profile nose, which remains unchanged and a profile tail section, which is transformed into an 8-phase sequence, using wavelength, and amplitude logarithmic spirals of generation applied to isocline acceleration control points on the median chord. These can displace the envelope-shaping chord-normal rays of graphic construction. The ends of these displaced rays are subsequently connected by cubic spline curves. This phase fragment is then mated to the Archimedes Spiral profile nose, which has been plotted relative to the truncated cone illustrated on the top right of FIG. 5c, to result in a 3-D ‘blade’, missing its tail sections. This Spiral nose ‘blade’, deemed attached to the surface of the cone, is then rotated by small increment via this cone, and the next—integral multiple—numbered phase fragment is again mated. This is repeated at equal angular increments of rotation of the cone until the entire length of the Spiral nose section has been filled with a multitude of full-cycle tail section sequences. These are subsequently connected tangentially with cubic spline curves, thereby blending their transitions. Upon rotation, the resulting surfaces' tangential motion through the axial plane-of-shear, provide a smooth rate-of-change variation of chord-transverse inclination over the rear portion of the profile, as is shown on the bottom right of FIG. 5d, whereas the axial-plane-relative flattening slope of the isocline parabola provide for the desired acceleration of the body-relative transverse wave.
A full sequence of these phase fragments in its motion through the plane of shear is a Meta-Element as is shown in FIG. 5c. In its effect on the axially aligned predominant momentum of flow, it can be visualized as an infinitely flexible, very thin, but nevertheless physical film—being composed of a slippery membrane of segregated and viscous material—that closely adheres and animatedly responds like a glove to the rate-of-change isoclines of this resonator sequence in its tangential path through this plane. As the resulting entire 3-D spiral ‘blade’ is attended by this physical film, boundary layer turbulence, profile drag, as well as induced drag is diminished when compared to conventional blades by the propulsion mechanism of anguillar locomotion.
The Meta-Element is thus deemed physical in the sense that it is made up of many layers of physical viscous lubricant matter, reconciling inner tangential to outer axial flows. It is deemed permeable at the back to allow for the expulsion of lubricant accumulations. In the manner of a thin rubber glove it responds to the changing angles of inclined planes that tangentially transition through it, by converting this rate-of-change to shear plane-relative profile-transverse impulses in space quadrature through force decomposition as is shown on the lower right of FIG. 5d. 
In this sense, it acts the part of the oil film contact patch of the spiral worm gear of FIG. 8e that converts rotary motion to the linear motion of its conjugate rack, using the same tangential-to-axial motion conversion mechanism. Since this resulting Meta Element motion thus effectively duplicates the mechanism of anguillar propulsion in space quadrature vector conversion, it is attended by the well documented ‘reverse’ Karman Vortex Street containing the observed central jet and bounding vortices as illustrated.
To ascertain whether this phenomenon is in fact ‘real’—and not some form of wishful thinking—, I measured the wake rotation of my physical fan prototype and found that wake rotation was less than the commercial fan it replaced. As the measured wake rotation was very modest, I could conclude that lubricity, the axial shear plane, and the Meta-Element itself are mutually interdependent, real phenomena.
To analyze this configuration in operating mode, conditions of shear drag are first estimated using published data attending viscosity and velocity of flat plate drag. The dynamic forces of profile drag attending this published profile are then used to offset the designed small increment of anguillar thrust and the—very—low induced drag estimates are added. Finally, the lift equation is used assuming axial-plane-relative velocity composed of the vector sum of axial and radial spiral motion components. To this is added the vector component of incoming axial flow. This process is shown in FIG. 13d, where the resulting vector diagram is compared to a diagram of a conventional turbine.
The resulting lift equation-derived differential pressure forces are conventionally attached normal to the variably inclined spiral-derived profile-sequence's surfaces, as is shown in the lower half of FIG. 13d. They are then corrected for their angle of orientation relative to the axial plane to determine the resulting turning moments acting upon the rotor axis of motion. This is also shown on the bottom of FIG. 13d. 
Being a device of rotation, however, there is little doubt that physical profile sections must travel in helical paths in order to provide these described—or envisioned—artifacts.
There cannot, by definition, be two dynamic flows, namely one attending helical motion and another as the result of some secondary artifact thereof. This presented a great conundrum in my initial investigations of these devices. I therefore examined the resulting blade elements' relative aerodynamic shape, orientation and velocity vector sums. This is shown in FIG. 6. Each resulting individual profile shape helical section is entirely anomalous, having different values of chord length, thickness, camber and after-body kink depending on its distance from the axis of rotation and the intersected after-body phase range. They were all, however, of recognizable fluid dynamic shape. Moreover, their angle of attack of helical motion was largely self-similar and closely within a range of Meta-Element orientation to axial flow. Their velocities, being the vector sum of local radius rotational velocity and that of axial flow, were however, significantly lower at all radial locations including the outermost in the case of the wind turbine configuration. Based on these facts, I computed a worst-case scenario contribution to—or detraction from—this helical motion and found a largely non-existent contribution to Meta-Element differential pressure and considerable detraction due to form drag.
As only a single field of differential pressure can exist around single fluid dynamic surfaces, and the Meta Element's spiral advance vector-sum-based relative velocity is designed to be greater than that of helical motion, I concluded—and subsequently proved to myself—that the modest adversity attending helical motion of anomalous profile changes does not disable the greatly increased differential pressures and efficiencies of the Meta Element.
To sum the relatively ancillary effect of helical motion on this spiral based devices:                1. The physical device actually shears through the axial plane at linear velocities that greatly dominate helical velocities. Fluid must part around this axial plane progression and create the velocity-appropriate classical pattern of dynamic lift, thereby overwhelming ancillary helical influence.        2. As shown in on the lower right of FIG. 6, during a given time slice, all isobars attending helical motion have an attenuated effect directly ahead of motion, thus weakening inflow and upwash via a sector of diffusion as defined by the helix-tangents swept during that time, whereas linear motion isobar influence extends durably and with relative concentration, thus providing additional reason for the linear motion dominance of influence over helical motion.        
Having now proposed the definition of the physical Meta Element and its interdependent relationship with the axial plane of shear as a rate-of-change quantifiable process, it can now export these quantities in a familiar parameter form as bridge concept, or plug-in, enabling use of the classical analytical framework of momentum theory, as well as conventional pressure/velocity oriented tools such as those of Helicopter Blade Element analysis for additional refinement.
To demonstrate the theoretical operational advantages of these spiral-based devices using the parameters of analysis of classical perspectives, I refer to FIG. 13c, which is a 2-dimensional representation of the total streamline flow field attending the spiral ‘blade’ as just previously described and illustrated on the upper left of FIG. 5c. This is shown as being attached on one end to a body of revolution and on the other end to an annular wing, which in turn is mounted upon this body via tensile spokes. Although only a single blade is visible for the sake of visual clarity, several such ‘blades’ should be deemed similarly attached at equal angles to provide symmetry. A tower—not shown—holds this rotor assembly and a tail vane—again not shown—allows the axis of revolution to align itself parallel to flow direction and largely prevent wake twist.
Upon rotation, a single Meta Element—as being composed of the slippery, viscous film with which its axial shear plane counterpart has surrounded it—moves as shown along a path that is defined by the radial and axial coordinates of its rotor ‘blade's’ truncated cone-coordinate remapped coaxial Archimedes Spiral-of-generation. This path orientation is shown underneath the conic spiral of FIG. 5c. As all other co-axial planes and their Meta Elements are simultaneously generating the same orientation, velocity and thus dynamic flow patterns, these multiplicities can therefore me modeled as forces attending a single axial datum plane.
The vector sums of this motion and axial streamline components, as well as the force resultant of this motion are plotted to provide a dear visual metaphor on the lower left of FIG. 13d. This resultant is then decomposed into components of turning moment versus downwind force. These values are then compared with known operating parameters attending conventional turbines in the same drawing. These are seen to generate comparatively large downwind forces. It is seen on the lower right that when compared on the basis of equal amounts of downwind force—called thrust in wind turbine practice—this vector decomposition shows that the Meta Element device, using very conservative values of spiral axial advance, generates several times the turning force per aggregate of downwind force.
As some of these large conventional turbines must be designed to be able to sustain loads approaching a hundred tons, these vector decompositions make clear that they extract a relatively small amount of energy at the expense of relatively great amounts of mass flow linear momentum that they make unavailable to themselves and to downwind turbines.
This in turn illustrates the phenomenon of the upwind and downwind expansion of the theoretical stream tube 90 of left FIG. 13b predicted by Momentum Theory, which limits the amount of energy capture of this stream tube to the well known “Betz Limit” of approximately 59 percent of the theoretically available power attending the mass flow rate available in this ‘tube’, a limit that has in fact never thus far been exceeded by any conventional device.
To illustrate the Momentum Theory implications upon these proposed devices, I now refer to FIG. 13c, which has re-oriented the Froude or Rankine Actuator Disc 20 of FIG. 2—which reflects the plane of orientation of the swept disc of rotating ‘sails’ or ‘blades’ in a usage of convention dating back for several thousand years—into an Actuator Cone of modern duct configuration reflecting the actual swept surface of orientation of the moving spiral ‘blades’ on the left of FIG 5c. 
As—for purposes of pressure-velocity-relation based analysis—the original Froude Actuator Disc is deemed semi permeable and composed of an infinity of rotating blades, so too is this Actuator Cone of FIG. 13c deemed open a the front and composed of a semi-permeable conic membrane—exactly as in the Actuator Disc—that extracts a given quantity of momentum in exchange for a given amount of impulse of turning force. As is seen, its orientation allows a simple flow-net analysis of flows that reflects its property as a duct of fluid continuum, allowing upstream and downstream control volume adjustment and energy conservation.
The resulting low-pressure isobar orientation just outside of the contracting semi-permeable surfaces of the Actuator Cone—as per Bernoulli—Theorem-based derivation—causes the original stream tube core to be enveloped by an additional outside stream tube mantle, which is decelerated by the shallow angle of deflection into this low-pressure region.
This decelerating stream tube mantle's sacrifice to total upstream and downstream momentum loss must therefore be approximately twice that of the sacrifice of the original ‘inner’ stream tube, as estimated by the relative contribution of low-pressure versus high pressure to the total differential forces attending the generation of all lift.
These two flows are thus seen to be mirror images of one another as seen in the lower diagrams of the diagram of variations of pressure and velocity attending each. They are thus deemed synergetic and mutually geometrically enmeshed.
The Actuator Disc is a legacy concept predating modern boundary layer theory as well as predating Duct Theory of Computational Fluid Dynamics. ‘Stretching’ it into an Actuator Cone via the rule-based transformations of topology, which recognizes these surfaces to be in an important sense identical when plotted with a stretched time axis, is mathematically defensible and provides considerable theoretical advantage:                1. For a given extraction—or exchange—of momentum, it spreads the deflective impulse of extraction—instead of over the volume of a blade-wide thin disc—to the much greater volume of mass flow exterior to, as well as within this duct of conic shape itself. It also does this over a much longer time, as fluid particles need more time to cross this extractive mechanism as compared to the time needed to cross the thin Actuator Disc. Thus mass-flow-specific impulse, deformation shear and downwind force per given values of power extraction are much lower.        2. In the case of wind turbines, the analytical convention of the Actuator Disc concept itself has imposed a strategy of erecting a massive barrier to flow, which can be up to twice the equivalent swept area of a flat plate. This imposes many tons of blade root and tower base forces requiring expensive means to assure rigidity, resulting in devices whose aspect is industrially stark and obtrusive, provoking proven public resistance to these harsh intrusions upon cherished pristine and pastoral landscape. The Actuator Cone based devices on the other hand, have a very low tower load and so could slowly sway upon slender towers, steered by their tail vanes. Here they would no longer be limited to decelerating a single stream tube, but rather an incoming elliptically expanding funnel of arc of oscillation, involving even greater mass flow and thereby extract more energy. The period of this sway could be coordinated in a networked synergy in the case of a wind farm to allow greater total energy for turbines operating downwind. Importantly, this quaint motion, reminiscent of trees, along with the inherent sculptural qualities and visual continuity of spiral motion might well disarm some aspects of public objection.        
To summarize, as Blade Element vector analysis shows, the proposed duct/spiral-based device extracts several times the turning force for a given amount of downwind force as compared to he conventional wind turbine. As the rough calculations using the parameters of Momentum Theory and Duct Theory show, the impulse of power extraction through deflection is transferred to an interlocked stream tube system that involve up to three times the mass flows rates considered by the Actuator Disc.
As power extraction is a relation of impulse to momentum, these devices spread this impulse to greater mass flow rates and do it without the unintended consequence of converting linear momentum into the chaotic angular momentum of turbulence of FIG. 3.
Thus, it has become evident to myself and will also become apparent for anyone who has access to the tools of lift analysis and the flow net, that the Betz Limit—as being an artifact of the legacy orientation of the Actuator Disc and affecting a stream tube of Disc diameter—is not directly applicable to this duct-based device, which should exceed this limit.
As will be shown subsequently, in its function as a device of propulsion, the Meta Element device will demonstrate increased thrust-per-torque and through the ability to tailor resultant forces, will allow operation at flight velocities previously unattainable by the convential propeller by simple reorientation of the Actuator Disc into an Actuator Cone using truncated cones and spiral parameters.
This has now concluded the exposition of the theory of operation affecting the entire family of these proposed devices' common theoretical operating principles. What follows is a more detailed perspective on the theoretical operational aspects of specific applications. To teat these with full justice, some of the same ground must be restated, in order that the ambiguities due to the lack of extensive mathematical format be eliminated as much as possible.
Since the Meta-Element in motion on both dimensions of the totality of axial planes is an expression of a time series waveform with its harmonics that in its operating cycle encloses a volume 94 as shown in FIG. 13c, it opens the possibility of using the normally unavailable out-of-phase potential kinetic energy of periodic harmonic oscillation of this resonantly coupled volume of fluid mass.
This is accomplished by correctly phasing impulse trains from the Meta-Element cascade of successive passage to benefit from the momentum of phase shifted fluid elastic rebound 59 exactly as it occurs in nature, as is shown in FIG. 8e. 
FIG. 7d further illustrates tis concept. An incrementally consecutive Meta-Element phase fragment series on the right is designed to follow the contour of a periodic wave. The operating angle at which the Meta-Element meets oncoming flow is thus a function of compound waveform, path wavelength 44, intercepting the shorter incidence wavelength 46.
As it is a well-documented prime prerequisite for the efficient development of high forces that this angle be kept a constant as possible throughout the operating range, these proposed devices make use of a periodic function for a cosine wave that includes an infinity of odd numbered harmonics. As was shown previously, this slope can also be generated by path resultants 45 of a Spiral of Archimedes, when remapped to truncated conoids-of-revolution.
This motion generates constant operating angles of inflow, except at the short reversal sequence, where the Meta-Element ‘changes tack’, i.e. reverses its orientation to the inflow and generates a vortex of reversal.
The passage of the resulting ‘blade’ in forward motion can be visualized in its effect on the axial plane of stationary fluid. Here, as is shown in FIG. 7a, any single waveform concavity/convexity forming the resulting time axis topological helix ‘worm’ rotating forward at axial velocity will stay stationary relative to particles on this plane, while the topological ‘worm’ as a whole moves forward.
The back-to-back truncated cones, with their spirals-of-generation, are deemed rotationally enmeshed with this single ‘worm’ concavity as is shown in FIG. 7b. Progressive rotation of these conic spirals generates a stationary conoid convexity relative to this stationary plane. Progressive profile phase elements are plotted as phase angle harmonic integral multiples of the fundamental angular velocity of these cones-of-generation's surface. This sequence is illustrated as axial progression 52 of FIG. 7c and retrogression 54 of FIG. 7a as well as their relative advantages—depending upon application—in the ability to tailor force vector alignments that minimize/maximize torque or maximize useful forces. Since these forces attach normal to spiral surfaces, final vector decomposition must be corrected for the average spiral angle of inclination of these surfaces.
When compared to the conventional propeller vectors in FIG. 1, it is seen that these devices generate more thrust-per-torque by being able to direct greater amounts of final forces in the desired al direction and by apportioning thrust loading 78 more evenly across its swept cones of actuation as is shown in FIG. 11.                1. A full 360-degree cycle thus constitutes a full cycle Meta element        2. An integral harmonic subcomponent of this wave within the frequency range of natural eddy formation—known to fluid dynamicists as Strouhal number—is superimposed in the form of a harmonic sub cycle sequence 48 generated by using a parabolic envelope of maxima 50 for the harmonic component transpositions of increasing amplitude, re-mapping the aft portion of the mean camber line.        
Finally the vector-shear based momentum transfer of the boundary layer is computed using flat plate equivalents, or from the equations of Navier-Stokes.
The effect of this momentum transfer on the deformation of the Meta-Element shear plane is finally ‘steered’ by stabilizing it through the variation of the major out-of-plane force modifiers such as sweep and surface pressure gradient in an iterative recursion.
To explain schematically the advantages conferred by the ability to detach the Meta-Element orbital flow field pressure wave from the underlying physical surface, I refer to prior art as show in FIG. 8.
Here a conventional wind turbine flow field—redrawn from the contours of an actual photograph of the wind tunnel streamlines as delineated by smoke trails—is compared with the flaw field of the Meta-Element based axial plane spiral based system of oscillation.
The conventional air turbine generates power by creating a well documented highly turbulent, noisy field of enmeshed, interlocking masses of turbulent air that counter-rotate 64 in a self-reinforcing system that persists far downstream.
The impulse of blade passage upon the inertially interlocked incoming axial stream tube of initially exclusive axial momentum that generates this phenomenon thus creates an intermittent angular momentum reaction that is related in magnitude to these sharp impulses 58 of episodic angular acceleration of single direction.
The blades of this turbine encounter air that is therefore already in the process of accommodating itself to this rotation in a phenomenon well known to designers of such devices as ‘blade cascade interference’. This effect manifests itself in reduced inflow vectors 56. This concept is metaphorically similar to the idea of birds of passage flying in the sinking air of their preceding leader, rather than laterally displaced, in their classic V formation.
Another metaphor would be idea of letting the angular kinetic energy imparted to a rotating toy disc on a string—a ‘YOYO’—in the form of angular momentum, to go to waste, rather than use it to cause the disc to climb back up the string.
By contrast, the wind turbine designed according to Meta-Element time series polarized oscillation creates the classic low-turbulence reverse Karman vortex street, the source of the documented unequaled efficiency of creatures of nature.
It accomplishes this by varying the interplay of the major parameters of influence that determine Meta-Element wave period, harmonic overtone, shape, orientation and thrust as well as the boundary layer influences that determine Meta-Element orientation. Finally, it largely neutralizes tangential components of force by using a variety of means to prevent flow excursion from purely axial motion.
The effect of these axial plane velocity and acceleration vectors then attach to the inclined surfaces in the form of dynamic differential pressure patterns that create tangential forces by acting at right angles to the inclination of these surfaces.
Additionally, in this way, does the potential energy contained in the moment of momentum of the oscillating fluid reaction mass become available to the phase-shifted cascade of successive rotor passage.
The benefits of such a scheme is manifold:    1. Fluid reaction masses arrayed in the highly patterned, coherent and low turbulence Karman wave-vortex pattern—as shown in the upper portion of FIG. 8e—are documented to rapidly widen and attenuate, thus involving a higher reaction mass with a lower mass specific impulse, unlike the propellers high specific impulse's counter rotating turbulent wake which forms a self insulating system that continually dissipates kinetic energy and persists in time.    2. A highly patterned system of bi-directional time-series oscillations can be exploded by the Meta-Element—free to move in both dimensions of the axial plane by choosing the timing of succeeding passages to occur out-of-phase 59 as in FIG. 8e—, thus recapturing some of the kinetic energy potential of the oscillating inflowing fluid mass and also conserving more kinetic energy of the air tube as a whole. A similar effect is used in nature by all migrating birds as well as schooling fish that benefit from reaction pressure waves created by their neighbors, as this is a form of ‘free’ energy. The effect of this for the Meta-Element turbine is a significant increase in torque per fluid momentum loss through beneficially shifted force vectors 60. This is schematically shown in the relatively attenuated wave/vortex system downstream.    3. Unlike a propeller, which imparts sharp, episodic, and staccato impulses 58 on that axially arrayed limited mass of fluid confined to the immediate vicinity of its operating disc of actuation, the Meta Element, in its oscillating motions simultaneously and synergistically interacts with a much greater fluid reaction mass that has been set in polarized resonant oscillation in all axial planes of the azimuth. Thus the Meta-Element device spreads its impulse bad to a much greater mass flow resulting in a smooth, non-pulsing surge 53 analogous to a spiral gear-rack conjugation, when compared to the spur tooth pulsations of single tooth engagement.    4. Finally, a turbine employing a soliton wave engendering Meta-Element progressing axially forward 59—against the ambient fluid stream—will generate significant increases in differential pressure intensities resulting from this vector addition as this wave front ‘virtual’ velocity will be significantly higher than ambient stream velocities. The resulting higher pressures act on intermediating spiral surfaces and the resulting beneficially shifted force vectors 60 provide greatly expanded torque per given fluid momentum loss, permitting highly unusual values of torque per unit of downwind as well as blade drag.
To summarize Meta Element time considerations:    1. Meta-Element hypothesis conceives of all bodies—whether rigid or not—that are interchanging impulses with fluid mass momentum as sharing contours with a dynamic flow that has the character of a non-linear damped pressure wave system that can be expressed as a Fourier series periodic function. This periodic function includes those harmonic subcomponents that produce the characteristic resonant vortex shedding at the tail. This entrains periodic vertical flexion of the vector field that cycles faster than hysteresis based system frequency response. It views the phase plane spiral curves of this oscillation as an information source for values of body-relative viscous friction.    2. All fluid dynamic bodies are therefore deemed an integral part of a phase locked oscillating system involving fluid masses exhibiting the fluid dynamic equivalents of resistance, capacitance and inductance. Since the particles of such masses move in elliptical or circular orbits, such oscillations interchange angular momentum with such bodies, and thus have mechanisms to conserve this angular momentum. But as is shown in FIG. 13a, since any rigid object—especially a rigid tail—cannot accommodate itself to the high frequency wave potentials of the small waveless harmonic component sub orbits, it develops an interfering phase lag with the prime wave component, causing these disordered high frequency energies to precipitate into rapidly pulsing vertical moments 61 at the tail. This results in the formation of a surface of discontinuity that acts as a barrier to the phase path continuity of particle orbits. Significant high frequency components of angular momentum of the bound vortex are discharged into this roiling surface of discontinuity, creating a highly concentrated area of dissipation through small scale turbulent intermixing. This phenomenon distorts the waveform, and degrades oscillation-rebound-based mechanisms of energy conservation through phased elastic energy recovery.    3. As is shown in FIG. 13a, the conventional propeller is additionally burdened by a secondary consequence attending this surface of discontinuity, as the divergent flows 61 of the upper and lower surfaces fail to rejoin at the trailing edge and so develop distortions of the surface of discontinuity that terminate in medium scale vortices containing high levels of lost energy in the form of moment of momentum.The wake of fishes is known to contain much smaller amounts of vorticity and turbulence, allowing them their observed unequalled efficiencies. Thus, strategies here outlined include Soliton Meta-Element tail flexion to re-export lost capacitive energies to the flow, restoring the coherence of the oscillating system through feedback of lost short wavelength harmonics.
Meta-Element hypothesis thus sees the induced wake losses of the rigid tail conventional propeller as being the result of an unintended conversion of significant energies of impulse to disorderly angular moment of momentum.
This, in turn allows the coherent wave attending lift to become disordered and so to discharge some of its moment of momentum into a cascade of chaotic flows of decreasing scale. This cascade ends in generating useless heat and sound. In doing so, it also provides a ready escape for the waste of meaningful amounts of kinetic energy that might otherwise remain available.
It is the primary goal of these methods to interrupt this specific causal chain.
These strategies, however, use the momentum transfer of fluid shear props of the lubricating boundary layer as the principal enabling mechanism.
This layer's behavior in flows containing shear-in-vector and turbulence is unfortunately not presently fully modeled by the scientific community.
Thus, the possibility existed that these strategies, however promising, might well lack insight on some unexpected detrimental interactions, and thus unintended consequences.
For this reason I set out to build such a device. I first generated the unusual coordinates of a propeller device by computer program. Because of paucity of means I confined the design to purely radial motion. This design also did not include the harmonic spiral sub oscillation, or axial motion.
However, this prototype construction of an electrical fan using a propulsive element made by these methods showed good correlation with the predictions of this model and provided significantly greater airflow, thrust, flow coherence, less near and far wake turbulence as well as significantly less noise than the commercial fan blade it replaced. Precise measurements of electrical consumption, velocity and near and far wake area show significantly greater mass airflow per torque with a blade not incorporating above mentioned boundary layer scavenging features.
Compared to other axial flow devices, propellers use relatively large and thus efficient impulses on large mass flows of fluid.
The proposed innovation extends this idea even further. It also operates on large masses of fluid. But it operates completely unlike a heavily tip-loaded blade, which intermittently imparts sharp energetic pulses of varying radial intensity to local axial fluid stream tubes and then leaves the locality entirely for the rotational part cycle until its return.
This phenomenon imparts the characteristic clapping noise, pressure pulsations, and vortex formation with counter rotating inner core, induced drag and sharp velocity variations, flow reversals and pressure peaks of the wake.
Thus, the stream tubes proceeding parallel to any given axial plane in the proposed invention constantly remain within the influence of the transiting phase sequence of the Soliton Meta-Element as it travels at constant speed and constant angle of attack. All other axial planes simultaneously experience the Meta-Element in different synergistic phases.
In all such planes, they experience neither the entire absence of the Meta-Element from their locality of influence at any moment, or significant pulsation nor therefore intermittence of impulse, thus generating less noise and compensatory vortex flows.
All other coaxial strata are simultaneously experiencing the Meta-Element in complementary phases traveling at the same speed and angle of attack.
Therefore, all fluid stream tubes in the whole of the annulus swept by the half loop embodying the Meta-Element experience an analogous constant non-pulsating and relatively evenly distributed surge 53 of FIG. 8e. 
The previously described deficiencies of propeller devices are addressed by the following schematic of strategy:    1—Using an absolutely even distribution of pressure field propagation velocity of the Meta-Element caused by its Archimedes' Spiral Cam-induced radial and axial excursions—not in the rotational but the axial plane—. A high and even velocity across the axial plane predicts even and correctly aligned pressure loading across most of the annulus, thus minimizing cross flows. Additionally, a significantly greater portion of torque is converted to thrust through the improved resultant vectors in the axial direction.    2—Eliminating blade tips. As is shown in FIG. 8, a given local companion Soliton pressure field constantly follows the reversing spiraling Mete-Element back and forth; it lacks the opportunity to discharge potential energy into conventional tip vortex formation. The starting vortex of reversal 55 that is generated is of much smaller intensity, as the phase shifted successive passages attenuates it Without significant tip vortex formation, less induced downwash wake rotation 64 together with improved element orientation 60 combine to significantly reduce wake corkscrew, pulsation and noise.Summary of this Compound Motion:
The thin lubricating sheath of the boundary layer combined with the inertia of coherently oscillating flow ‘memory’ of hysteresis substantially prevents the rotational motion of the catenary half loop embodying the spiral cam and sequence of resonators from substantially deflecting the dynamic flow.
Therefore the Meta-Element presents the inertially dominating preponderance of local plane axially aligned fluid, —itself resistant to immediate angular deflection reaction by reason of its overwhelming inertia—, with the sustained presence-in-time of a moving wave of rarefaction, accompanied by one of compaction, moving along both dimensions of the axial plane of motion as shown in FIG. 8.
To accommodate their passage, axial stream tubes have no other choice but to divide around this phenomenon in the classical pattern of high and low velocity flows that generate the differential pressures of lift.
Since a local soliton bound-vortex wave propagating on the axial plane experiences the transition of successive ‘resonators’ sliding through its plane as a local moving shape in the process of shape transformation, this ‘virtual’ shape animated by the transiting wave-resonator-train thus cannot leave its orbitally and inertially coupled axial plane fluid stratum.
Thus, the temporarily contained differential pressures—generated by the high and low velocity stream division—have no opportunity to discharge. This is much unlike the case of the propeller where the containing surfaces—i.e. the open propeller blade tip—suddenly leaves the locality entirely.
Here they can implode into a high velocity tip vortex, precisely at the location where the sudden, explosive appearance of the highly loaded propeller tip is followed by its equally sudden, implosive local disappearance.
As there is no open tip, there are no preconditions for pressure-induced, wasteful, implosive and noisy vortex flows.
The third source of improvement over the conventional propeller based device deals with the phenomenon of the boundary layer itself.
In any foil generating lit, the dynamic flow surrenders some of its kinetic energy to envelop what it sees as an obstacle to its smoothly energy-conserving flow with an appropriate lubricating envelope.
The fluid particles that make up this envelope are few at the nose of the foil and slide over each other in smooth ‘lamina’ 41 generating low drag as shown in FIG. 10.
Soon however, depending on prevailing viscosity, —through the mechanism of frictional entrainment—these intermix and accumulate to a thick envelope of violently turbulent particles 21 that are continuously losing momentum to heat and creating large scrubbing drag coefficients. The boundary layer export to dynamic flow of frictional drag is thus cumulative and therefore exponentially concentrated toward the tail.
At some point of their passage particles lose enough momentum to lose their resistance to random motion, especially in conditions of low viscosity. Here they start to oscillate and impinge on strata of different energy levels and even reverse their motion, pooling in a time-based tidal accumulation toward the trailing edge.
This phenomenon increases drag through the mechanism of violent vortex-based intermixing of layers of different levels of retardation causing high velocity scrubbing of the surface and thus high frictional drag.
In conditions of high lift, or high Mach number and thus adverse pressure gradients, boundary layer material accumulates on the back of the suction side of the foil and eventually flows backward, forming pockets of accumulation.
This ultimately causes the dynamic flow to detach from the surface, resulting in premature loss of lift, high drag and premature stall.
Even using moderate operating lift coefficients, the wake of a conventional propeller contains a wide band—‘vortex sheer’—of this slowed material roiling with spiraling eddies which ultimately rolls up into large diameter tip vortices causing the well documented losses due to induced drag.
The accumulation of boundary layer material can thus be appreciated as among the main constraining parameter of design of all lifting devices. Without consideration of the boundary layer, the practice of fluid dynamics would not be possible.
Thus the very conceptual foundation of the proposed invention's designed mode of operation is the attempt to influence the development and relive extent of this layer. These concepts analyze the relative retardation of this slow moving layer as a tidal flow, as being time based and cumulative.
As shown in FIG. 13c, the proposed invention uses this property of the relatively slow accumulation of such material to advantage by presenting the pervasive low pressure field existing ahead of and all across the entry to its swept annulus area with the rapidly shifting sides—and isobars—of the propulsive element going through its spiral reversals. Rapidly shifting isobars predict less tidal cumulative flow of boundary material, as it is sustained pressure differentials over time that is the prime causal factor of such accumulations.
The underlying physical surfaces sliding through a given axial plane of the virtual element do in fact entrain additional boundary layer particles and thus generate additional viscous drag, but these experience neither steady nor uniformly adverse pressure gradients, as they constantly encounter rapidly changing pressure gradients. This encourages larger regions of laminar flow, which is known to exhibit much lower drag than turbulent flow and can thus more than compensate for the effects of this additional shear velocity.
As is shown on the right of FIG. 7d the traveling wave sequence of spiral corrugations 48 on the after body of the physical profiles, —the Meta-Element phase fragments—additionally impart a wave train of transverse flexion of the virtual element tail section.
They employ that requisite Fourier harmonic hysteresis based wave frequency and amplitude and expanding wavelength that can scavenge such boundary layer accumulation through means of the resulting rapidly traveling pressure wave packets.
They additionally use the geometric distributing action of the high frequency transverse flexion of the tail tip. This deforms the 'sheet of discontinuity’ of FIG. 13a into corrugations that help to prevent slowed boundary layer segregation by physically distributing it to larger regions of dynamic flow.
Absent a steady unfavorable pressure gradient, the conditions for tidal boundary layer accumulations are also relatively absent Hence, more lift for less viscous drag.
As becomes evident from FIG. 10, any such boundary layer control—here enabled through the novel sliding interaction with axial plane orbits 51—is known to present opportunities of operating with drag coefficients that can be a fraction of those lifting foils operating with mostly turbulent boundary layers.
Additionally, it has been proven that any such boundary layer ejection—using any available method—allows the generation of unusually high lift coefficients before flow separation. Well-documented experiments with a belt 65 as shown in FIG. 10 moving in the direction of flow, allowed angles of attack approaching 90 degrees before stall.
Removing such boundary layer material by suction 52 has been proven to achieve similar—though less dramatic—effects.
In these here-proposed devices, such boundary layer effect is implemented by superimposing an integral harmonic waveform with an exponentially expanding envelope limiting amplitude and wavelength on the tail section of the Meta-Element. The resulting harmonic wave motion contains specifically tailored energies to overcome expected viscous losses.
This envelope is constructed as s-led by the differential equation governing the term of viscous dissipation phase plane logarithmic spiral. This waveform of exponential maxima envelope 66 progressively affects only the aft envelope median of the Meta-Element as shown in a visually exaggerated schematic in FIG. 10. The actual affected area is generally limited to the aft half chord of the tail section itself.
The resulting hysteresis parameter oscillation harmonic subcomponent results in a traveling ripple 86 of FIG. 11 along the tail of the virtual element 82 at exponentially increasing velocity and amplitude.
This wave thus acts in the manner of a peristaltic pump by creating a traveling pressure pulse referenced to relative Meta-Element chord percentage at a speed referenced to local dynamic stream velocities that forcibly conveys slowed boundary material back toward the rapidly flexing tail of the Meta-Element.
This latter action widely distributes this slowed material to regions of the free stream that have the energy potential to readily reaccelerate it. This effectively thins the wake through four mechanisms:                1—These traveling corrugations of the Meta-element tail section reconcile the boundary layer velocity differentials shown in FIG. 13a involving the upper and lower rejoining streams through their equal velocity pressure wave propagation        2—The hysteresis based high frequency of vertical flexion which attenuates natural periodic eddy formation—at Strouhal Number frequency—by preempting its motive cause, being the progressive accumulation and periodic shedding of slowed boundary layer material        3—The geometrically extended trailing edge with its vertical component of hysteresis-referenced motion—and physical orientation—benefits thrust vectorially from the unequal lateral components of the flows above and below the trailing edge and        4—The extra physical trailing edge length resulting from the spiraling wave train terminating in trailing edge diagonal corrugations enables greater momentum transfer due to a physically wider admixture of the upper and lower flows—as mediated by the longer interface of these rejoining flows of differing lateral and axial velocities above and below the camber neutral axis.        
This has the effect of a momentum transfer based substantial interlocking, enmeshing and reconciling of these two flows of inequality of axial and lateral momentum by minimizing and physically disrupting the insulating and separating barrier sheet of discarded highly turbulent lubrication—the ‘vortex sheet’—of FIG. 13a that normally bars this re-enmeshment.
This action substantially reduces this thin sheet of wake discontinuity made of shed viscous boundary layer material that normally separates laterally and axially divergent upper and lower flows.
If these rejoining flows have less divergence of axial and lateral momentum, such smaller residual differences will cause significantly less local axially oriented vortex development and its associated turbulence and drag.
Since this is a phenomenon well documented in the wake of fish, such strategies may well also benefit these proposed devices in an analogous fashion.
A further significant benefit is the restoration of the energy conserving mechanism of wave oscillation, which depends on the phase completion of integral particle orbits 72 as shown in FIG. 11 that make up its motion. Since all harmonic wave components of wavelengths shorter than the length of the Meta-Element will be prevented from completing their natural orbits as a consequence of physical passage, only such proposed Meta-Element harmonic flexion can reconstitute these missing harmonic components. Such a scheme prevents the precipitation of this ‘disturbance of passage’ into the documented disordered flows of chaotic moment of momentum attendant to rigid tail passage.
As this vortex formation caused by vector divergence of rejoining flows is also known to be implicated in tip vortex formation, this method of boundary layer control theoretically affects every term of drag and loss of lift known to the art of fluid mechanics.
Such purposive procedural intervention—no matter what its ultimate degree of effectiveness—agrees well with academic theory that promises—and has experimentally proven—unusually large benefits from any method of removing boundary layer accumulations.
The employment of the momentum transfer of the sliding resonant element train for these novel pressure wave artifacts could not, however, be contemplated by an academic model using rate-of-change invariant rigid foil theory.
Prior art inventions that did not decompose axial and transverse velocity changes resulting from oscillation dynamics into phase plane parameters of wave frequency, propagation gradient, amplitude and envelope analysis, containing rate-of-change vectors, could not promulgate such procedural design elements, nor state their degree of expected benefit.
A shear-stressed, thin boundary layer is additionally less liable to early transition into turbulent flow states as its field of opportunity—large pools of accumulated boundary layer material with low inertia—is smaller.
Importantly, operations under conditions of high lift can be expected to improve dramatically if the boundary layer is given less opportunity to stop, reverse, and accumulate—a primary cause for breakdown of the dynamic flow and subsequent catastrophic stall or transonic buffet. Higher maximum coefficients of lift thus become theoretically feasible.
These procedurally derived shape variations have thus proven to be of benefit in responding to losses caused by phenomena previously thought unamenable in man made devices.
A significant element of advance promised by the design procedures of the proposed invention has to do with the ability of these methods to expressly design pressure gradients into the pressure recovery section of the virtual foil by means other than the conventional variation of pressure gradient, namely by the export of precise quanta of energy into the boundary layer by the exponentially expanding traveling wave 66 of FIG. 11.
Thus, until now, velocity profiles due to after-body shape camber variation and their resulting pressure gradients were the sole means of accommodating primarily boundary layer mediated phenomena.
These boundary layer scavenging methods here detailed now offer an additional technique to the designer of these devices resulting in new families of Meta-Element foil sections characterized by thinner and shorter laminar flow foils, shorter recovery sections, with optimized resulting force vectors resulting in less drag.
Benefit of Solution to Slip Stream Contraction Disadvantage:
Another element of advantage of the proposed invention has to do with the phenomenon of the contraction—or expansion in the case of the turbine—of the slipstream 22 as shown in FIG. 2 that is a source of efficiency losses in the conventional propeller-based devices.
This contraction occasions another loss deemed unamenable through built-in operating properties of the propeller, and yet is partially remedied and so is made to aid efficiency in the proposed invention through the following additional mechanism of benefit, entirely unanticipated by conventional practice:
As shown in FIG. 8, the Meta-Element benefits from a momentary angular orientation 59 to this inflow, due to the physical orientation of rotor surfaces. This benefits the transitioning Meta-Element significantly through the favorably shifted vectors of the contracting inflow providing it with vectors that the propeller discards. The benefit is three fold:    1—The increment of force resulting from the forward axial vector component 60    2—The lessened contraction of the actuator annulus—resulting from rotor peripheral surface orientation opposing such contraction—predicts an increment of efficiency through increased mass flow as well as increased peripheral differential pressures across the annulus allowing a higher ratio of torque to drag.    3—The purposeful containment of differential pressures at the periphery of the rotor by design ameliorates the chief cause of excessive induced downwash and thus high levels of induced wake rotation 64 of the conventional propeller. Additionally, since the small reversal tip vortex 45 rotates in space quadrature, it does not reinforce the comparatively small Meta-Element wake rotation 62, which thus can rapidly attenuate. Thus, the Meta-Element wake contains less wasted energy in the form of useless rotation of reaction masses.
Benefits through axial retrogression: cavitation and transonic flight—:
A further novel element of advantage has to do with the ability to so vary fore and aft deployment of the hub attachment of arched spiral segments 33 of FIG. 5c that the virtual foil of the Meta-Element of FIG. 7c is given an axial progression 52 or regression—FIG. 7d component 54 to its motion.
In the case of a propulsion device, use of an axial retrogression component significantly improves resultant force alignment with the axis of thrust beyond even its existing advantage, resulting in greater thrust for torque.
If the pressure wave propagation can be successfully disengaged from the resonant element train by careful adjustment of the parameters that cause proper Meta-Element axial plane radial orientation and thrust, the highly swept helical element tip sequence will experience apparent inflow neutrality and can thus travel at velocities that would otherwise cause the onset of compressibility phenomena.
As shown on the lower middle in FIG. 10, the compressibility shockwave 57 phenomena are a function of lift coefficient, as the lower surface in the transonic regime remains relatively unaffected.
This circumstance allows significantly higher operating velocities, as the helically oriented physical elements can be designed to experience flow neutrality in this region particularly, deriving thrust from relatively energetic tail sequence harmonic motion involving the relatively compressibility-immune aft foil section.
As forward axial velocity components can substantially diminish, or even actually vanish for the propagating pressure wave, the hysteresis artifact of the Meta-Element can operate in a purposely designed ‘virtual’ velocity regime, where the wave-front experiences only the much lower radial velocities. Here the actual fluid relative velocity through the modification of the local pressure wave ‘virtual’ velocity. Flight into velocity regimes previously closed to the propeller thus become theoretically possible.
In the case of a turbine, use of an advancing Meta-Element wave-front axial component results in significant improvements of power extracted from a given velocity of flow through the resulting substantial augmentation of resultant vectors' forward shift as shown in FIG. 13c, allowing higher torque components for a given retardation of flow. This predicts greater percentages of kinetic energy extraction from a given mass flow, using inner rotor counter rotation or a tail vane stator—to offset air steam listing moments.
This velocity and vector augmentation additionally favors power extraction from low wind speeds, as the Meta-Element apparent inflow velocity is greatly increased through the vector addition of spiral axial advance accompanying the Meta-Element As previously outlined, the air mass interacting with the turbine will experience significantly less momentum loss per increment of torque than the comparable conventional turbine through the beneficial redirection of force resultants so made possible.
Benefits Through Actuator Volume Mass Flow Increase:
Any conventional turbine's performance as a device that collects torque in exchange for some of the momentum of a theoretical column of air of rotor diameter extending ahead of it is calculated with a variant of “Momentum Theory”.
This theory substitutes a mathematical abstraction called “actuator disc” for the propeller's plane of rotation in order to circumvent the theoretical difficulties inherent in analyzing the extremely complicated interdependence of flows across this interface.
This theory's well proven expression for efficiency uses the geometric size of this actuator disc area together with mass velocity change in an equation that can be summarized as follows:
“The device using the greatest possible actuator disc area to effect the smallest possible mass momentum change has the greatest efficiency”.
From this point of view the Meta-Element turbine with its greatly increased actuator disc virtual array 92 of FIG. 13c enclosed in a volume 94 of fluid that counteracts its radial expansion, and thus predicts much higher efficiency from the terms of this equation.
Additionally, as illustrated in FIG. 13b, the column of air approaching the conventional propeller disc with its highly flow retarding pressure distribution, as well as its greater than ‘flat plate’ form drag co-efficient, must expand to accommodate its severe loss of velocity when it crosses the actuator disc plane.
This causes the effective tube diameter to decrease from its theoretical size identity with the rotor disc so that only a certain portion of the theoretical kinetic energy is actually available at the disc of actuation.
This phenomenon, described by the noted German aerodynamicist Betz in the early part of twenty century, has been a major factor in the so-called “Betz Limit”, a theoretical ceiling on turbine performance of a given diameter that has yet to be exceeded.
As becomes evident in by visual comparison in FIG. 13c, here exaggerated for clarity, the Meta-Element turbine, as compared to the conventional turbine—viewed simply as an obstacle to ambient flow—presents a much more fluid-dynamically favorable pressure distribution and aerodynamic shape to the approaching air that combine to favor ‘inflow funneling’ 37 and allows greater mass air flow for a given amount of flow retarding force coefficient.
This combination of features is designed to exceed such stated previous performance limits.
Additionally, since this proposed turbine constrains radial expansion of the approaching flow by means of such ‘Inflow Funneling’, it stabilizes any directional wind instabilities—such as yaw—though its negative pressure feedback mechanisms, which act in the manner of an aerodynamic duct.
Such yaw correction ability is of considerable benefit, since the conventional propeller-based turbine is known to severely lag in yaw-response that is known to impose severe performance and stability penalties.
The last advantage of the proposed invention has to do with its shape.
As shown in FIG. 9, an enclosed, highly triangulated rotor shape with its mutually supportive A-frame arches close to centrifugal catenary curvature offers a natural rigidity, comparatively high natural frequency and intrinsic resistance to dynamic, harmonic and Coriolis forces.
It does not need a massive blade root, as it experiences primarily tension throughout its operating envelope. It encounters little bending, torsion or blade tip interference phenomena.
Thus, its design has less need to compromise with structural consideration and can thus be much lighter, thinner and more fluid dynamically efficient throughout its length.
As a water propeller, this design offers built in resistance to foreign object fouling and cavitation without the need to sacrifice any efficiency to do so, unlike the conventional ‘weed-less’ propeller.
Due to its non-injurious shape, it can be used in certain applications previously closed to open tip propellers.
Additionally, its novel layered manufacturing methods 114 as shown in FIG. 23 allow minute air entrainment to further reduce friction and susceptibility to cavitation.
As it generates very little blade impulse phenomena and so is relatively immune to interblade interference, it can be located closer to hull or appendage, permitting increased diameter and thus even additional efficiency as replacement rotor in existing applications.
Benefits of Unprecedented Scalability and Economic Cost-benefit:
As the wind turbine rotor segments of substantially centrifugal catenary shape display high natural frequency and rigidity, they offer high resistance to strong or variable wind, and tower turbulence. As such ‘TENSEGRITY’ structures are subject primarily to tensile forces, they can be scaled to unprecedented physical size—and therefore economic viability—.
Benefits of Public Acceptability:
The Meta-Element turbine generates a low, steady, non-staccato noise footprint Due to its unprecedented lift over drag ratio, it operates economically in lower as well as higher wind speeds than conventional turbines. Unlike a conventional wind turbine, which can generate tens of tons upon its blade roots and massive tower, it generates relatively small amounts of downwind force, allowing it to store the energy of gusts in the deflection and energy storage of a slender fiberglass tower. As such motion, as well as that of the restful non-flickering, curved shapes, faintly whimsical motion of its spiral rotor is reminiscent of the motion of trees, so that one of the public-wide objections to conventional turbines' stark aspect of industrial sharp angularity and their overpowering obtrusion upon cherished landscapes may well be moderated.
Especially in its application in wind farms, it makes possible extremely cost efficient, small footprint installations of architectural and sculptural qualities that provide the esthetic value of an organic, natural form of low sound, low footprint, and pleasingly restful motion. Therefore it promises a likelier degree of public tolerance—the documented key to the wide adoption of wind power itself.
These benefits thus offer unprecedented, and—in the light of present and prior art—high cost benefit ratios.
Structural Advantages:
Conventional turbine blades have very low natural frequencies, as they are made of very slender, elongated, thin, unsupported strips of thus necessarily flexible blades.
These are intrinsically less resistant to torsion, experience high bending moments, and thus incur high levels of alternating stresses, resonant oscillations, flutter and fatigue.
Due to their length to mass ratio, large wind turbine blades are thus akin to a very long—and very expensive—resonant single prong tuning forks with intrinsically high root loads, susceptibility to inertial self-coupling and tower resonant coupling instabilities and so present formidable engineering challenges. They have very low angular velocity and so need expensive gear trains with their own elastic modulus and sensitivity to inertial shock and resonance.
They thus need equally expensive measures to compensate—such as upwind operation, employment of expensive exotic structural materials and methods of manufacture, complicated pitch changing mechanisms or teetering arrangements and massive blade roots with their weight and losses of efficiency.
Additionally, such wind turbines are notoriously difficult to control in regard to output regulation or resistance to high or variable winds and must simply be shut down at relatively moderate wind speeds, just when wind energy is most available. Their whistling noise, visual flickering, lack of esthetics, lack of wide public acceptance—and marginal economic basis—has prevented their wide-scale adoption in areas of less than high average wind velocity and low population density.
Thus they are located away from population centers and are limited to the few high wind locations that have adequately low property value or population density.
They therefore impose the additional expense of long distance electrical distribution on their economic cost basis.
Due to these factors—using the aforementioned relatively wasteful and expensive strategies—has a free natural resource of almost unlimited potential for the production of low cost energy that does not generate greenhouse gasses, so far produced only marginal and limited benefit to society at large.
Summation of My Solutions to Present Wind-generation Problems:
To summarize the tangible and intangible benefits of the proposed turbine:
If the world-wide stated public policy goal of wide-scale adoption of environmentally beneficial, cost competitive energy production methods could be viewed as achievable not only as the result of the development of economically successful devices offering relative cost-basis benefit, but also by offering such strategies that successfully address those intangible considerations affecting public acceptance and embrace, then these proposals will be seen to certainly offer improved tangible cost benefit of unprecedented degree.
They additionally offer unprecedented solutions to documented esthetic objection, which affect public readiness to embrace change itself.
They do this by offer a pleasing novel iconography of moving organic forms, curves and spirals that has the esthetic appeal, and soothing physiological impact of colorful kites dancing in the wind. They offer a visual experience that leads the eye along a predictable linear recurrence, non-flickering smooth trajectory, in an unbroken, non-staccato visual continuum. Documented visual mechanisms such as the persistence of vision can encompass such motion as a single unified totality.
As such it will tend to be inherently non-injurious to wildlife, as well as unlikely to provoke the built-in involuntary human physiological responses to the stroboscopic visual flickering of massive conventional turbine ‘blades’ that whistle the approach of a blade moving at guillotine-like velocities.
If such qualities then help to confer to these proposed wind turbines such unquestioned notorious benefit and lack of controversy as do—for instance—large trees, or equally large physical objects of art, or public monuments of architecture, then these devices, together with their tangible and economic benefits might offer a solution to a presently evidenced intractable public resistance that has—so far—prevented wide adoption of an eminently practical form of energy that is insensitive to supply constraints and price fluctuation.
To Summarize Schematically the Foregoing Background Exposition:
If turbines and propellers of present technology and proposed prior art are considered to be offering methods based on strategies and procedures of generating thrust—or torque—, these conventional methods offer procedures that passively tolerate:
Noise
A severely fluctuating and wasteful pressure field propagation velocity,                Resulting in wasteful force orientation and        High torque for low thrust in propellers—or high drag for low torque in turbines—        
High boundary layer entrainment,                Wasteful, turbulent vortex sheet of discontinuity,        Strong, turbulent tip vortex,        Actuator disc contraction, —or expansion in turbines—        
Limited lift coefficient,                Early transonic compressibility drag,        Induced wake rotation,        High levels of lost energy deposited as turbulence and noise.        High Cost of manufacture        Low esthetic value        Low public acceptance and tolerance        
In contrast these novel concepts offer a methodical procedure of using hysteresis and vector-shear to create axial-plane-polarized bound vortex orbital flows through successive embodiment sequences of resonator sequences to create:
Procedurally induced pressure field propagation direction and velocity and low noise
And procedurally induced boundary layer scavenging